Difference between revisions of "1990 AJHSME Problems/Problem 19"

(Created page with '==Problem== There are <math>120</math> seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone? <math…')
(No difference)

Revision as of 21:32, 11 July 2009

Problem

There are $120$ seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?

$\text{(A)}\ 30 \qquad \text{(B)}\ 40 \qquad \text{(C)}\ 41 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 119$

Solution

If there are $120/2=60$ seats occupied, then it is possible to get an occupation of the seats where no person sits next to someone else. However, the only way is through alternating seats.

Thus, if another person joins, two people must sit next to each other, so $\boxed{\text{D}}$.

See Also

1990 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 18
Followed by
Problem 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions